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Mathematics: AI SL

Paper 2

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Mathematics: AI SL

Available time 20 Minute(s)

Peter, the manager at JK cafe welcomes hundred of guests every week to his cafe.

Paper 2

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Available time 20 Minute(s)

01. Question

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Maximum Mark 8

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Peter, the manager at JK cafe welcomes hundred of guests every week to his cafe. To determine whether the number of guests are uniformly distributed among the days in the week, a random sample of 224 guests are studied for their days of occurrence. The results are shown below.

(a). Calculate the expected frequencies, on the assumption that each day should be equally proportional in calls received.

[Marks: 2]

(b). A $x^{2}$ goodness of fit test is performed at a 5% significance level.

(i) State the null and alternate hypotheses

[Marks: 1]

(b).(ii) Write down the number of degrees of freedom.

[Marks: 1]

(b).(iii) Using your graphics display calculator, find the $χ^{2}$ -statistic

[Marks: 1]

and p-value.

[Marks: 1]

(c). Given that the test is performed at a 5% signficance level. Determine the conclusion for the test, providing a reason.

[Marks: 2]

Reject H₀

Accept H₀

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